6.4 Implications for melt extraction timescales
From the solutions tabulated in tables 3 and 4 , we
also perform forward simulations that calculate the height of a
compacting column as a function of time (Fig. 14 ). A list of
the values used in these calculations is provided in table 5 .
The calculations are performed assuming an initial column height of 1 m
and extrapolates the viscosity values obtained in the inversions to a
grain size of 4 mm (Fig. 14 ). The results from Boyer et
al. (2011) suggest repacking laws don’t have an inherent dependence on
grain size, and therefore one of the curves plotted in (Fig.
14 ) has an identical \(\xi_{\text{ref}}\) to one of the curves plotted
in (Fig. 14 ). However, in the limit that the particle size is
sufficiently large with respect to the domain size, the presence of
ephemeral force chains may contribute significantly to the rheology of a
column of compacting particles. This is likely due to the boundary
effects which prevent particles from rotating and translating. This
effect is amplified as the particle size grows larger with respect to
the domain size Hoyos et al. (2022). Such grain size dependence
was determined from these experiments and found a power law exponent of
ca. 1.9 (Fig. 7 ). A curve assuming this grain size dependence
is calculated for the case of repacking and is also plotted in
(Fig. 14 ).